Papers

In this work we study the robustness of $\mathsf{QAC}^0$ with respect to error tolerance and modifications to its gate-set. First, we investigate whether the non-zero error typically allowed for $\mathsf{QAC}^0$ circuits computing Boolean functions is truly necessary. We show that the error inherent in the parallel $W$-test of \cite{grier_morris_wu} can be eliminated entirely via a novel application of exact amplitude amplification in the many-copies context. Consequently, we find that $\mathsf{QAC}^0$ can exactly simulate $\mathsf{TC}^0$ with polynomially many copies of the classical input and that for every fixed prime $p$ exact $\mathsf{QAC}^0$, $\mathsf{EQAC}^0$, can compute total Boolean functions outside of $\mathsf{AC}^0[p]$. Second, we ask to what extent the computational power of $\mathsf{QAC}^0$ follows from the fact that arbitrary single-qubit gates may be used at any point in the circuit. We find that $\mathsf{QAC}^0$ is in fact robust to restrictions on which single-qubit gates are permitted: every $\mathsf{QAC}^0$ circuit can be approximately implemented by a $\mathsf{QAC}^0$ circuit consisting of just generalized Toffoli, $S$, and Hadamard gates. Moreover, this approximating circuit can be constructed efficiently from a classical description of the original circuit.

Physical processes in solar flares span many orders of magnitude in spatiotemporal scales, so a single unified model accounting for all relevant processes remains computationally intractable. Instead, specialized codes have been developed, targeting specific domains that tackle specific aspects of the solar flare problem. Here, we present a comprehensive framework that links three models to capture flare initiation and energy release, the subsequent particle acceleration, the propagation and thermalization of those particles, and ultimately the heating of the lower solar atmosphere. We use the 2.5D ARMS magnetohydrodynamics (MHD) code to model stressing of the magnetic field in a simulated active region, the formation of a current sheet, magnetic reconnection, and the evolution of newly formed flare loops. We use the conditions in the ARMS' current sheet to initialize the kglobal model, which predicts time-dependent nonthermal electron and proton distributions. Finally, we use RADYN+FP to inject these distributions into a newly reconnected ARMS loop and compute subsequent particle transport, atmospheric heating, and radiative emissions. This is the first detailed presentation of a RADYN+FP simulation tracking nonthermal electrons and protons in the same loop. As well as discussing the interesting physics that takes place, we note how this results in white-light flare emission height consistent with observations. This work is a first step toward building a fully 3D flare modeling framework.

We give a deterministic classical algorithm that estimates $|\langle x|U|0^n\rangle|^2$ to additive error $\varepsilon$ in $\mathrm{poly}(n, 1/\varepsilon)$ time, where $U$ is a constant-depth quantum circuit comprised of gates with bounded fan-in and arbitrary connectivity, and $x$ is an arbitrary $n$-bit output string. This improves over prior state-of-the-art algorithms that takes $n^{O(log(n))}$ time for the same task, $n^{O(log(log(n))}$ when $U$ is geometrically local, and $n^{O(1)}$ for 2D geometrically-local circuits.

Decoded quantum interferometry (DQI) is a novel paradigm for tackling approximate optimization problems on quantum computers. This framework comes with strong performance guarantees and exploits a well-established duality between optimization and coding theory. A central question, however, is whether DQI can actually provably outperform all polynomial-time classical algorithms. In this work, we establish such an advantage in an oracle setting: we consider an optimization task called folded optimal polynomial intersection (folded OPI), where the acceptance sets are chosen randomly and accessed through membership oracles. We establish a strict gap between the approximation ratio achievable by any polynomial-time classical algorithm and the approximation ratio achieved by the DQI algorithm. Our proof builds on Jordan et al.'s DQI framework for approximate optimization and extends the classical lower-bound method underlying Yamakawa and Zhandry's exact-search oracle separation to approximation. Building on recent developments by Sun and Wootters, Horinaga and Yamakawa, and Jo, we further show that a modified version of the DQI algorithm achieves a strictly higher score guarantee on typical sampled folded OPI instances. As a concrete example, for code rate $0.3$, DQI achieves expected scores of approximately $0.85$. In contrast, exceeding the classical threshold of $0.65$ by any fixed amount with constant probability on sampled instances requires super-polynomially many classical membership queries.

Fluid models of discharges fail where electron runaway dominates. On the left branch of the Paschen curve and in high-voltage cathode sheaths, the electron population splits into a thermal bulk and a ballistic beam that no single electron fluid can represent. We present a multigroup fluid model that divides ballistic electrons into groups indexed by their birth potential: the electrostatic potential at which they were liberated, offset by the forward kinetic energy they carried. Because the birth potential is a constant of ballistic motion, the electric field never moves electrons between groups and only collisions do. Each group requires a single continuity equation because its velocity follows algebraically from the local potential, and the number of groups is set by the energy resolution alone independently of the mesh. A runaway criterion based on the local field assigns each newly liberated electron to the bulk or a ballistic group, so the model applies even where no sheath exists. Benchmarked against a kinetic solver in argon, it reproduces the left branch of the Paschen curve—which local-field and local-energy models miss or misplace—and tracks the current–voltage characteristic of a cathode sheath to within a few percent at reduced fields exceeding $10^4$ Td, where the local-energy model overpredicts the current up to thirtyfold. Since as few as 10 to 30 groups suffice, depending on the field, the approach brings near-kinetic accuracy to multi-species computational fluid dynamics solvers at the cost of that many additional species, without added velocity-space dimensions or particle noise.

We derive the canonically normalized modes of a two-field inflationary system with arbitrary constant quadratic mixing and unequal sound speeds $c_\varphi$ and $c_\sigma$ for the curvature and isocurvature perturbations, respectively. A Laplace representation reduces the coupled dynamics to a second-order Heun equation and gives the exact late-time curvature power spectrum for arbitrary values of the mixing parameter and entropy mass. The sound-speed ratio $r_c=c_\sigma/c_\varphi$ controls the separation between the two sound horizons. At fixed nonzero mixing and $r_c\ll1$, the power exhibits power-law enhancement, growth as $\ln^2(1/r_c)$, or bounded oscillations in $\ln r_c$, depending on the mass and mixing. For $r_c\gg1$, the correction to the unmixed spectrum vanishes as $\ln r_c/r_c^2$ at fixed mass and mixing. Using the same normalized modes, we compute the tree-level bispectrum for three representative cubic interactions, with the mixing parameter treated exactly. For heavy entropy fields, unequal speeds modify the collider amplitude and phase while preserving the strict squeezed frequency set by the final entropy mass. The power-normalized amplitude can vary nonmonotonically with $r_c$, and a sound-speed hierarchy can delay the approach to this asymptotic regime.

We first provide a simple proof showing that any single-shot code is self-correcting. We then show that any $[[n,k]]$ CSS quantum low-density parity-check (QLDPC) code can be transformed into an $[[nm,k]]$ CSS QLDPC code with single-shot (SS) quantum error correction and an efficient local decoder which runs in $O(\log m)$ parallel time. Below a constant threshold $p_{\rm RG}>0$ for joint local stochastic physical and measurement noise, the logical failure probability over $T$ correction rounds is bounded by \begin{equation*} O(T n)\exp[-\Omega(m^\alpha)] \end{equation*} for a constant $\alpha>0$; we say that the threshold is $p_{\rm RG}$ and error suppression is $\Omega(m^{\alpha})$. Moreover, if the input code is equipped with a single-shot decoder with threshold $p_c>0$ and error suppression $\Omega(n^{\beta})$, then the output code enhances the error suppression to $\Omega(m^{\alpha} n^{\beta})$, while maintaining the decoder-independent threshold $p_{\rm RG}$, and thus enhanced if $p_c < p_{\rm RG}$.

Unsupervised anomaly detection (UAD) methods for brain MRI are ranked by a single score, yet that score rests on choices that are rarely reported: how each anomaly map is aligned with the reference, how and on which data the threshold is set, and which false-positive budget, metric, aggregation and lesion definition are used. We present MIRTO, an evaluation protocol that makes these choices explicit and measures their effect. It gates the geometry of every comparison with a registration check and label-free diagnostics of known power, sets thresholds on validation data alone and reports the false-positive volume actually realised on test, repeats each comparison over 15,552 defensible evaluation pipelines, and attaches paired subject-bootstrap intervals with multiplicity control. Applied to four UAD methods trained on the same healthy data and tested on 312 BraTS 2020 subjects, MIRTO showed that an axis-order mismatch between stored maps and the reference lowered a diffusion model's voxel AUROC from 0.873 to 0.583 whilst barely moving its slice-level AUROC. Within each metric, the method explained at least 0.95 of the variance in voxel AUROC and AUPRC and 0.77 in Dice, but only 0.14 in lesion sensitivity, where the lesion definition and hit criterion dominated. A Dice advantage that was significant at validation thresholds vanished at equal realised false-positive burden, and an exact identity attributes it to threshold transfer. A training-free change to REFLECT's latent aggregation raised Dice at equal burden by 0.052. Nine hypotheses were tested against explicit criteria; because the same cohort served to develop the protocol, all inference is exploratory.

Random quantum circuits aim to efficiently reproduce the statistical properties of ideal random quantum evolution. One approach is to construct approximate unitary designs, which match the moments of Haar-random unitaries up to a prescribed order with controlled error. In this work, we establish quantitative guarantees for how accurately these designs reproduce the full distributions of individual output probabilities. We show that, for every strong $\varepsilon$-approximate unitary $k$-design on $n$ qubits, the distribution of each individual output probability is within $O\left(\sqrt{\frac{2^n}{k(k+2^n)}}+\varepsilon\right)$ in Kolmogorov distance of the finite-dimensional Porter-Thomas distribution, a beta distribution with parameters $1$ and $2^n-1$. This bound is optimal up to constant factors, implying that a substantially better uniform bound requires additional structure. We further show that local invariance yields an exponential improvement in the dependence on $k$, with guarantees also in the stronger metric of total variation: every strong $\varepsilon$-approximate unitary $k$-design invariant under unitary translations acting on $\log k+O(1)$ qubits achieves error $2^{-\Omega(k)}+O(\varepsilon)$ in Kolmogorov distance and $2^{-\Omega(k)}+O(\varepsilon\log(2/\varepsilon))$ in total variation distance. These results identify both the distributional accuracy guaranteed by moment matching and the additional structure that substantially improves it. As an application, we show that if the marginal distribution of each output probability of a strong approximate design is within Kolmogorov distance $\eta$ of its Haar counterpart, then the expected Shannon entropy of the output distribution differs from its Haar value by $O(\sqrt{\eta})$.

We prove a generalized quantum Stein lemma for i.i.d. normal states against convex, tensor-stable families on arbitrary von Neumann algebras. Assuming the existence of an alternative state with finite relative entropy from the null state, we show that, at every type-I error tolerance $\varepsilon\in (0,1)$, the worst case type-II error exponent is achieved with the regularized relative entropy with a strong converse. The proof combines the integral representation of relative entropy by hockey-stick divergences, a modular testing bound, and convex minimax argument.

Transducers (Belovs, Jeffery and Yolcu, 2024) are a quantum computing framework describing a quantum algorithm as a unitary converting an input state into a target state using a catalyst, an auxiliary vector that is left unchanged. They are a powerful tool in quantum algorithm design, especially in the context of quantum query complexity: feasible points of the (dual) adversary semidefinite program directly translate into transducers and the optimal transduction complexity is equal to the adversary bound, i.e. the Las Vegas complexity, which is known to characterize bounded-error quantum query complexity. Moreover, contrary to bounded-error algorithms, transducers compose exactly, which limits overheads due to controlling errors in algorithms constructed by composition. Constructing efficient, let alone optimal, transducers in terms of quantum query complexity nevertheless remains a hard task since it still requires solving the adversary SDP and constructing the unitary to obtain an explicit algorithm. In this paper, we show how using the symmetry group of state-conversion problems simplifies both steps. First, using a symmetrization argument, we prove an optimal catalyst can always be chosen covariant under a representation of the symmetry group. Second, we prove that the transducer intertwines two different representations of the group and can thus be chosen block diagonal in the isotypic decomposition of the Hilbert space. Using those methods, we then derive optimal transducers, with optimal constants, for different widely used quantum algorithmic primitives, such as unstructured search, amplitude amplification and amplitude estimation. Our approach extends previous work on the use of representation theory to compute adversary lower bounds (Høyer, Lee, and {\v S}palek, 2007; Ambainis, Magnin, Roetteler and Roland, 2011) to the systematic construction of optimal algorithms.

Purpose: To demonstrate how diffusion blurs the longitudinal magnetization in steady-state gradient-echo imaging, quantify resolution dependence on flip angle and repetition time, and the effects on relaxometry at microscopic resolution. Methods: Diffusion was incorporated into the Bloch-Torrey equation in $k$ space to determine how the point spread function (PSF) of $T_1$-weighted spoiled gradient-echo images varies with flip angle. Theoretical predictions were validated numerically and extended to b-SSFP. Results: Diffusion acts as a low-pass filter whose width depends on the diffusion rate ($D$), repetition time (TR), $T_1$ and flip angle ($\alpha$). The blurring length spans from $\sqrt{D \cdot \mathrm{TR}/2}$ at large $\alpha$ to $\sqrt{D T_1}$ as $\alpha \rightarrow 0$, equaling $\sqrt{D T_1/2}$ at the Ernst angle. Consequently, multi-angle acquisitions have mismatched resolution (PSF widths of 39 $\mu$m at $\alpha = 10^\circ$ versus 11 $\mu$m at $\alpha = 80^\circ$ for TR = 50 ms). For the flip-angle pair optimizing variable-flip-angle $T_1$ mapping, the effective resolutions differ by a factor of 2.4. In simulated DESPOT1 maps the $R_1$ of a 30 $\mu$m feature is reduced to 1.80 s$^{-1}$ (true value 2.00 s$^{-1}$). In b-SSFP, blurring depends on $T_1$, $T_2$, and $\alpha$ but is independent of TR, with a minimum of $\sqrt{D T_2}$. Conclusion: The PSF of a steady-state sequence depends on the flip angle and $T_1$. Combining images acquired at different flip angles implicitly assumes identical spatial resolution, but that is not valid at microscopic scales, affecting the accuracy of quantitative relaxometry. The theory identifies a new limitation on the ultimate resolution of MRI set by diffusion.

A quantum impurity model describes a small interacting subsystem embedded into a large bath of free fermions. Here we study the computational complexity of calculating the ground energy, thermal equilibrium, and dynamical properties of these models. Our work reveals a sharp contrast: equilibrium properties can be efficiently approximated by classical means, whereas time evolution can implement a universal quantum computation. More precisely, let $H$ be the Hamiltonian of an impurity model with $n$ fermionic modes and a constant-size impurity. We show that: (1) the ground energy of $H$ can be approximated to additive error $\varepsilon$ by a classical algorithm with runtime $\textsf{poly}(n,1/\varepsilon)$, improving on the quasi-polynomial runtime of the best previously known algorithm; (2) at inverse temperature $\beta$, the Helmholtz free energy and a classical description of the thermofield double state can be computed to precision $\varepsilon$ in time $\textsf{poly}(n,\beta,1/\varepsilon)$; (3) simulating the time evolution $e^{-iHt}$ is $\textsf{BQP}$-complete, for $H$ that is time-independent and has a fixed, constant impurity size. Our algorithms exploit exponential suppression of multi-particle bath excitations in a basis organized by energy scale and Krylov depth. Our universality construction realizes a stationary quantum processor whose program arrives in a stream of freely propagating fermions.

Fast and accurate qubit-state assignment is essential for feedback, calibration, and error correction in quantum processors. In superconducting platforms, frequency-multiplexed readout makes this task intrinsically multivariate as measured traces can encode crosstalk, qubit-state relaxation events, and other transient nonidealities that are not fully captured by conventional matched filtering. Here, we introduce spiking neural network (SNN) discriminators for superconducting qubit readout. By processing the measurement window in successive time chunks, the networks exploit temporal structure and update classification scores as data arrive, rather than waiting until the end of the readout window. The spiking networks outperform matched-filter discrimination and approach the accuracy of a full-trace artificial neural network. Beyond reaching the performance of artificial neural networks, the key advantage of SNNs is that they provide a streaming, time-resolved estimate of the qubit state that evolves as the readout signal is acquired. Using quantisation-aware training and hls4ml synthesis, we further demonstrate that each FPGA inference update can be completed before the next readout chunk arrives. These results establish spiking neural networks as a promising route to low-latency, real-time qubit readout on FPGA hardware, with broader implications for time-critical quantum-control and scientific-inference applications.

Porter-Thomas statistics are a characteristic feature of the output distribution of random quantum states and, more broadly, chaotic quantum many-body systems. Convergence to Porter-Thomas plays a central role in random circuit sampling and experimental demonstrations of quantum advantage, where the output statistics of low-depth random quantum circuits are expected to be approximately Porter-Thomas, despite the absence of a rigorous proof of convergence. We show that the output distribution of polynomial-depth brickwork random circuits converges inverse-polynomially in total variation distance to the Porter-Thomas distribution. Specifically, consider the output probability distribution over a fixed bitstring of a local random quantum circuit, constructed from nearest-neighbor Haar random gates. Then, for any $m \geq 0$, the distribution corresponding to circuits of depth $O(n^{2m+1}\log(n))$ is at most $O(1/n^m)$ far in total variation distance from the Porter-Thomas distribution. Our proof uses moment bounds from approximate designs, analytic estimates for characteristic functions, and a local anticoncentration property for inverse moments.

Recent work has shown that maximal supersymmetry, combined with a particular scalar-parity condition at six points, imposes nonlinear constraints on four-point effective field theory amplitudes. Numerical bootstrap studies incorporating unitarity provide evidence for the Veneziano amplitude in maximally supersymmetric Yang–Mills theory and for the Virasoro–Shapiro amplitude, together with infinite-spin alternatives, in supergravity. In this paper, we establish these constraints to all orders in the low-energy expansion. The derivation uses a collinear limit in which three three-particle factorization channels, or six in gravity, simultaneously go on shell. A scalar-parity projection and a single discrete R-symmetry eliminate the unknown six-point remainder, leaving three-term master equations determined entirely by four-point factorization. Solving these equations proves the conjectured exponential forms and provides a map that reconstructs the full amplitude from its regular forward limit. Under explicit analytic and positive dispersive assumptions, the fixed reflection-even part of the gauge-theory exponential determines the forward spectral measure and uniquely selects the Veneziano amplitude, with finite-spin residues emerging as a consequence. In gravity, the exponential leaves the forward measure undetermined: a measure supported at a single massive level reconstructs an amplitude with infinitely many exchanged spins at that mass. Finite-spin support at the lowest massive pole is therefore an additional assumption required to select the Virasoro–Shapiro amplitude within the stated ultraviolet framework.

We introduce information-theoretically private quantum protocols for two-party Hamming distance when both parties must output the same estimate. Classically, for input length $n$, information-theoretic protocols require $\Omega(\sqrt{n})$ error under pure differential privacy and $\Omega(\sqrt{n}/\log n)$ error under strong approximate differential privacy, whereas computational security permits $O(1)$ error. In Klauck's honest, nonpreemptive, message-preserving model, we give an $O(n)$-communication quantum protocol with pure $\varepsilon$ quantum differential privacy (QDP) and expected error at most $\frac{2}{\sinh \varepsilon}+\gamma$, for every $\gamma>0$. For approximate $(\varepsilon, \delta)$ QDP, an exact hockey-stick divergence calculation yields strictly smaller error, while preserving the $O(1)$-versus-$\Omega(\sqrt{n}/\log n)$ separation for $\delta=o(1/n)$. Thus, quantum communication achieves $O(1)$ information-theoretic error, matching the accuracy available classically only under computational assumptions. The main construction uses a guarded coherent round trip and an equal-Gram rigidity principle that prevents an honest player from retaining input-dependent complementary information. We separate this model from weaker prescribed-channel privacy, which already admits an exact classical realization, and from fully retention-robust security, against which measurement-and-abort attacks remain possible. Therefore, we identify preservation of non-orthogonal quantum messages as a resource for privacy.

We study resonance expansions and localised long-time dynamics for three-dimensional semiclassical Dirac operators. For smooth Hermitian matrix-valued perturbations which are analytic outside a compact set, we first obtain exponential cut-off resolvent bounds away from the resonance set and polynomial bounds in thin resonance-free rectangles adjacent to the real axis. Combining these estimates with a local $\Oc(h^{-3})$ upper bound on the number of resonances, a pigeonhole selection of admissible contours, almost-analytic functional calculus, and a Cauchy–Green deformation, we derive resonance expansions for spectrally localised propagators. Positive-energy resonances contribute for large positive times, whereas negative-energy resonances contribute for large negative times. We then specialise to mass-type perturbations $\mbf{\beta}V(x)$ in a nontrapping energy window. Using the logarithmic resonance-free region established in our earlier work together with a quantitative FBI-transform/escape-function argument, we obtain a polynomial bound for the continued cut-off resolvent and deduce rapid local-energy decay. We subsequently refine this polynomial estimate by a finite-time propagation argument in the undistorted region. Introducing the maximal positive-sheet connection time $T_\chi$ associated with the spatial cutoff, we prove a geometric continued-resolvent estimate and, for every fixed $M$ below the resonance-free depth constant, derive the explicit local-energy decay threshold $T_N>T_\chi+(N+1)/M$. The same analysis gives a rigorous microlocal obstruction to a uniform $[h\log(1/h)]^{-1}$ bound for the full distorted resolvent and identifies a finite-flight-time amplification mechanism for the sandwiched continued resolvent at logarithmic depth.

Deriving simple and accurate three-flavor neutrino oscillation probability formulas in matter is critical for understanding the phenomenology of upcoming experiments. In this article, we extend the Jacobi diagonalization method for deriving effective parameter mappings for neutrino oscillations in matter. The key insight behind the extension is to purposefully parameterize the mixing matrix, $U_{\text{PMNS}}$, using particular arrangements of Euler rotations. This novel extension allows for deriving simple and accurate effective mixing parameter mappings for exotic types of matter potentials. First, we revisit the Jacobi diagonalization method for neutrino oscillations with standard matter effects and use this to demonstrate our generalization. Subsequently, we apply the Jacobi diagonalization method to scalar non-standard interactions (SNSI) and derive effective parameter mappings for all three single diagonal coupling cases. The resulting formulas reveal that all diagonal SNSI couplings could give rise to a scalar MSW (SMSW) effect, that is an energy independent resonant enhancement analogous to the MSW effect. Finally, we study the accuracy of the derived SNSI formulas for various contemporary and upcoming experiments. For $\delta m_{ee}$, the accuracy is excellent for all considered experiments. For $\delta m_{\mu\mu}$ and $\delta m_{\tau \tau}$ the accuracy is worse since $A_{CC}$ must be neglected, and first order perturbative corrections are applied to amend this.

Density waves in gravity-driven granular pipe flow reduce transport efficiency and produce large fluctuations in the local solid fraction. Helical wall textures suppress these instabilities but at the expense of reduced throughput. Using discrete element simulations (DEM), \RefA{we find that this homogenization is associated with} spiral particle motion induced by the helical wall texture. Quantifying this motion by the mean angular velocity reveals a strong correlation between spiral motion, flow homogenization, and transport performance. Motivated by this insight, we introduce a helical pipe whose centerline follows a helical path while maintaining a constant circular cross section. This design generates stronger spiral motion than conventional helical wall textures. For suitable design parameters, the helical pipe simultaneously enhances flow homogeneity and increases the mean flow velocity beyond that of a plain straight pipe. These results support spiral motion as a useful diagnostic and design variable for simultaneously improving flow homogeneity and transport efficiency within the investigated parameter range.

We present a framework for propagating systematic data mismatches into parameter biases and posterior deformations beyond the Gaussian Fisher approximation. Using the Derivative Approximation for Likelihoods (DALI), we derive analytic expressions for the maximum a posteriori (MAP) point and posterior mean, including a semi-analytic response expansion in systematic amplitude. We validate the framework against direct numerical calculations and Markov Chain Monte Carlo (MCMC) sampling in a controlled nonlinear two-parameter benchmark up to a covariance-weighted data-space mismatch of $d_{data}=5$. At $d_{data}=5$, Fisher predicts the wrong direction of the shift in one parameter and differs from the numerical result by a Fisher-metric distance of 23.1, whereas the analytic DALI MAP prediction remains within 0.091, with componentwise errors of 0.04% and 0.46%. The response expansion reproduces the posterior mean with errors of 0.02% and 0.18%, while the DALI posterior closely reproduces the displacement and deformation of the fully sampled nonlinear posterior. Mismatches of equal significance but different directions produce markedly different parameter shifts and posterior deformations, while multiple additive mismatches can produce nonadditive parameter responses through nonlinear inference. By reconstructing the posterior under systematic mismatch, the framework captures the nonlinear response and non-Gaussian geometry of parameter bias: how mismatches move and reshape the posterior, why their direction matters, and how their combined effects can be dissected to understand the interplay between multiple systematics.

Schur sampling is a fundamental primitive for extracting permutation-invariant information from many-body quantum systems and has broad applications in quantum information science. Circuit-based implementations typically rely on coherent representation-theoretic operations such as Clebsch-Gordan transforms, generalized phase estimation, or quantum Fourier transforms over the symmetric group. We show that unitary Schur sampling of arbitrary permutation-invariant mixed states on $n$ $d$-dimensional qudits can instead be implemented using only pairwise SWAP tests, namely, two-qudit projective measurements onto the symmetric and antisymmetric subspaces. Our protocol achieves error $\epsilon$ in diamond distance using $O(n\min\{n,d\}^{3}\log^2(n/\epsilon))$ random SWAP tests. The central idea is to repeatedly identify and extract the largest antisymmetric subsystem. This turns unitary Schur sampling into a search for antisymmetry and gives the algorithm a natural interpretation as a stochastic traversal of a Young diagram. The protocol preserves the $\mathrm{SU}(d)$-irrep state while preparing a canonical pure state in the multiplicity subsystem. As an application, we consider quantum purity amplification (QPA), in which multiple noisy copies of a pure quantum state are combined to produce a state of higher purity. We show that the optimal purified state can be obtained by retaining a single designated output qudit and discarding the rest.

We prove near-optimal lower bounds for preprocessing attacks on quantum cryptography in the random oracle model. Specifically, we show that a $T$-query adversary with $S$ qubits of non-uniform advice can recover a random key $k$ from the $n$-qubit binary phase state $|\psi_k\rangle \propto \sum_{x} R(k,x) |x\rangle$ with probability at most $O(\frac{T^2 + \sqrt{ST}}{N})$ for $N=2^n$. In contrast, the best known bound for post-quantum one-way functions is $O(\frac{T^2 + ST}{N})$, with a trivial attack at $S = N$. This demonstrates a new advantage of quantum cryptography over classical cryptography: $n$ qubits of communication suffice for security against preprocessing attacks with space up to $N^2$ rather than $N$. Our methodology is simple: express the optimal preprocessing attack as the operator norm of a random matrix, and bound this value in expectation over the random oracle via the trace-moment method. These trace moments have a natural interpretation using compressed oracles [Zhandry, Crypto 2019], which we then analyze. This can be viewed as a simplification and generalization of the approach of Liu [Eurocrypt 2023] for proving the security of post-quantum cryptography against preprocessing attacks. We also prove the following results: (1) We tighten Liu's analysis of post-quantum PRGs in QROM, achieving a distinguishing advantage bound of $O(\frac{T^2}N + \sqrt{\frac{ST}N})$. (2) For unitary synthesis, we extend the one-query lower bound of Lombardi-Ma-Wright [STOC 2024] to hold against adversaries that can make one arbitrary function query along with polynomially many (adaptive) queries to the random oracle, either before or after the function query. This also interprets the original LMW24 result in terms of compressed oracles. (3) Finally, we prove a tight $O(\frac{\sqrt{S}}N)$ bound for the pseudorandomness of random binary phase states against space $S$ distinguishers.

Can simple processes appear highly complex? Gowers (Comb. Prob. Comp. '96) conjectured that repeatedly composing local random reversible operations can yield global permutations that are indistinguishable from random. In this work, we study the unitary quantum analog of this question, in an attempt to make new progress on this longstanding conjecture. Our first result shows that statistical moment matching in the form of unitary designs does not generically lead to pseudorandomness—even for the simplest quantum processes: for every fixed $t$, we give an efficiently samplable family $\{\nu_n\}_n$ of distributions on one- and two-qubit gates such that, after $T=O_t(n^2\log^2 n)$ independent steps, the resulting $n$-qubit ensemble is an approximate unitary $t$-design with negligible error $\exp(-\Omega(\log^2 n))$, yet an efficient quantum algorithm distinguishes it from random using only $O_t(\log^2 n)$ queries. This refutes the unitary analog of the Hoory–Magen–Myers–Rackoff conjecture (ICALP '04) for permutations. Our second result is a stronger separation between unitary designs and pseudorandom unitaries at polynomially bounded moments; our counterexample, however, requires highly structured ensembles, in contrast with the simple local walks from before. This suggests caution when using unitary designs to model information scrambling in black-hole physics, as even maximally scrambled systems can exhibit structure which is accessible to efficient experiments. Motivated by these findings, we then propose new conjectures for how pseudorandomness can plausibly emerge within simple quantum processes, such as random quantum circuits.

A longstanding question in quantum communication complexity is whether some task can be accomplished with a small amount of communication in the presence of entanglement, yet require much more quantum communication in the absence of entanglement. Separations of this nature were previously known for relational problems and, in the simultaneous message passing model, for partial functions. But it has remained unresolved whether any such separation exists for a total Boolean function. We resolve this question with an exponential separation in the one-way setting: we exhibit a family of total Boolean functions $f_n\colon \{0,1\}^n \times \{0,1\}^n \to \{0,1\}$ that can be computed with $O(\log n)$ bits of one-way classical communication given prior entanglement, but that require $\Omega(n^{1/3})$ qubits of one-way quantum communication without entanglement. Our function is a special case of the subgroup membership problem, first studied in the communication setting by Aaronson, Le Gall, Russell, and Tani.

Electromagnetic duality in the toric code has order two at the level of anyon types and acts as a Hadamard-type logical transformation on the encoded quantum information. Here, we ask whether it can likewise be realized microscopically as an order-two Clifford operation. For the $\mathbb{Z}_2$ toric code, we prove that any locality-preserving Clifford realization of electric-magnetic exchange cannot have order two. Our proof is fully general and requires neither translation symmetry with restricted families of system sizes nor a fixed pairing between vertex and plaquette stabilizers. Geometrically, the proof locally emulates the unavoidable crossing between electric and magnetic strings, similar to a cross-cap in a non-orientable manifold. Extending the problem to the $\mathbb{Z}_N$ toric code, we find that an order-two Clifford realization exists for odd $N$, whereas it is impossible for even $N$. Our results show that the group law of an emergent electromagnetic duality need not lift faithfully to its microscopic Clifford realization.

We present a global determination of the six long-distance matrix elements (LDMEs) within non-relativistic QCD (NRQCD) appearing in the production of prompt $J/\psi$ up to $\mathcal{O}(v^2)$ using high-$P_T$ LHC data for direct and feed-down contributions from $\chi_c$ and $\psi(2S)$. Using a leading-power fragmentation framework at NLO+NLL, we fit $\psi(2S)/J/\psi$ yield ratios from ATLAS and CMS and $\psi(2S)$ CMS polarization data at $\sqrt{s} = 13$ TeV, injecting one decay width per charmonium. The fit LDMEs provide excellent predictions of the CMS and ATLAS cross-section data up to $P_T=360$ GeV for the $J/\psi$, as well as the $J/\psi$ polarization data from CMS. The obtained excellent agreement with production and decay data demonstrates that $\mathcal{O}(v^2)$ NRQCD is sufficient to describe $J/\psi$, $\psi(2S)$, and $\chi_c$ hadroproduction at large $P_T$.

The quantum state preparation problem is to, given a description of a quantum state, efficiently generate a quantum circuit computing the state. We show that for quantum states described by weighted d-DNNF (deterministic, decomposable pseudo-Boolean circuits) a quantum circuit computing the state can be obtained in linear time up to complex arithmetic.

Symmetric private information retrieval (SPIR) lets an inquirer obtain one specific bit only, without leaking any information about its index to the database owner. With a single server, this is impossible for parties with unrestricted quantum power. We show that it becomes possible, with information-theoretic security, when the server and the user hold only noisy intermediate-scale quantum (NISQ) devices without long-term quantum memory and measure each qubit on arrival, while the eavesdropper remains all-powerful; this is a stricter form of the memory restriction of the bounded- and noisy-quantum-storage models. The server sends BB84 states one way; the user discriminates them unambiguously and so knows a random subset of the bits. After a joint random permutation into blocks, the user announces the conclusive locations of one privately chosen block, and the server hashes and takes a random parity of these locations in every block; the permutation makes it exponentially unlikely that one set of locations fits two blocks. We prove secrecy against the eavesdropper, database privacy through an explicit size rule for the announced set, and user privacy against a server who prepares the prescribed BB84 states and announces truthfully, exactly for single photons and up to a small multi-photon term over a tolerated noise channel. The only addition to BB84 equipment is a passive linear-optical measurement with one ancillary mode. For a $10^{4}$-bit database and database privacy $10^{-6}$, blocks of about a thousand qubits suffice over a tolerated noise channel for a user who applies the prescribed measurement; certifying an arbitrary memoryless user and committing to the permutation need larger auxiliary transmissions, which we quantify with finite keys. Database privacy extends to decoy-state weak coherent pulses, and simulations show that the bound is nearly tight.

A stationary scalar correlation energy admits an exact one-mode terminal representation even when the microscopic correlated return is strongly multimode. We test predictive realizations built from specified stationary information carriers in two complementary two-electron systems with the same Coulomb repulsion but different confinement: He-like ions and harmonium (Hooke's atom). For the Coulomb sequence, canonical RHF supplies the symmetry-faithful information carrier. The repeated same-mode return gives a He correlation error of $+0.1164$ m$E_{\mathrm h}$ and no more than $0.0157$ m$E_{\mathrm h}$ for Li$^+$–Ar$^{16+}$; H$^-$ is nevertheless bound and $93.3\%$ of its conventional correlation energy is recovered even though the RHF carrier is qualitatively strained. The dimensionless confinement factor $R_{CC}=D_{CC}/Z$ tends to $1.092394$. For harmonic confinement, an independently constructed response-compressed one-mode return gives $R_H=D_H/\sqrt{\omega}$; for $\omega\ge0.1$ it agrees with reference-inferred values within $0.21\%$ and tends to the literature high-density limit $1.309283$. Cioslowski and Pernal locate the qualitative crossover to the radially localized strongly correlated harmonium regime at $\omega_{\rm crit}\simeq0.04012$, below the quantitative domain used here. The H$^-$ endpoint and $\omega_{\rm crit}$ are therefore complementary carrier-validity boundaries: they limit the predictive realization, not exact terminal one-mode representability. A broad helium Bethe–Goldstone spectrum confirms that this terminal statement is not microscopic one-pole dynamics.